I am currently studying tensor networks, constructed from perfect tensors, introduced in article http://arxiv.org/abs/1503.06237
I would like to consider tensor network, which is holographic code. So as a setup we have some particular state on the boundary, state in the bulk(logical state) and tensor network which realizes map between two corresponding Hilbert spaces.
I believe that for different bulk states one should obtain different geometries of corresponding tensor networks. (I am particularly interested in considering vacuum and thermal CFT on the boundary)
I am trying to check this fact by means of calculating length of geodesic which corresponds to some region on the boundary.
My problem is that (according to my understanding) algorithm introduced in the aforementioned article gives the same result for all cases. According to it length of geodesic is a function only of number of cutted inplane lines along curve and their dimensionality.
Lengths of these geodesics can't be the same because these two tensor networks correspond to different geometries of the bulk.